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How to factor #2x^2+x-1# ?

i tried to factor it and i got #(2x+1)(x-1)#
but my friend said the correct answer is #(2x-1)(x+1)#

1 Answer
May 10, 2018

Answer:

#2x^2+x-1=color(blue)((x+1)(2x-1)#

Explanation:

Factor:

#2x^2+x-1#

The method to use is called "splitting the middle term."

Multiply the coefficient of the first term by the constant.

#2xx(-1)=-2#

Find two number that when added equal #1# and when multiplied equal #-2#. The numbers that meet the criteria are #2# and #-1#.

Rewrite the expression, splitting the middle term #x# into #2x# and #-x#.

#2x^2+2x-x-1#

Factor out the common terms in the first two terms and the second two terms.

#2x(x+1)-(x+1)# #larr# #-(x+1)=-1(x+1)#

Factor out #(x+1)#.

#(x+1)(2x-1)#